Question

Factor completely. y2 - 12y + 32 A. (y + 4)(y + 8) B. (y - 4)(y - 8) C. (y + 18)(y + 2) D. (y - 18)(y - 2)

Answer 1

Ask: Which two numbers add up to -12 and multiply to 32?

-8 and -4

Rewrite the expression using the above

= (y - 4)(y - 8)

Answer 2

The correct answer is option B.

Explanation:

Given quadratic equation :
`y^2-12y+32`

Using middle term splitting theorem:

=
`y^2-12y+32`

=
`y^2-8y-4y+32`

=
`y(y-8)-4(y-8)`

=
`(y-8)(y-4)`

y = 8, 4

The factors of given quadratic equation is (y-8)(y-4).